基于分而治之法的超约束多体系统反应唯一性分析

IF 2.6 2区 工程技术 Q2 MECHANICS
Marcin Pękal, Paweł Malczyk, Marek Wojtyra, Janusz Frączek
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引用次数: 0

摘要

对于具有冗余约束的刚性多体系统,由于计算反作用力的非唯一性,数学建模和对所获结果的物理解释都会受到阻碍。因此,唯一性分析对于评估结果的真实性至关重要。迄今为止,基于修正的运动方程、约束矩阵或自由体图而开发的唯一性检查方法并不十分适用于由相对坐标描述的多体系统。本文讨论的新方法打破了这一限制。所提出的方法基于分而治之算法(DCA)--一种用于复杂多体系统动态模拟的低阶递归方法。所设计的方法可用于检查具有理想约束条件的整体动力学系统的联合反应唯一性,并满足一些附加假设。反应唯一性分析在 DCA 的主通道完成后进行。提出了一种八步算法。在单关节连接的情况下,只需研究适当的运动方程即可。但是,如果存在多关节连接,则必须使用基于约束矩阵或基于自由体图的数值方法之一,即等级比较法、QR分解法、SVD法或无效空间法;所有这些方法都将进行讨论。为了说明所设计的方法,我们分析了一个带有三摆的空间平行四边形机构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Divide-and-conquer-based approach for the reaction uniqueness analysis in overconstrained multibody systems

Divide-and-conquer-based approach for the reaction uniqueness analysis in overconstrained multibody systems

For rigid multibody systems with redundant constraints, mathematical modeling and physical interpretation of the obtained results are impeded due to the nonuniqueness of the calculated reactions, which—in the case of load-dependent joint friction—may additionally lead to unrealistic simulated motion. It makes the uniqueness analysis crucial for assessing the fidelity of the results. The developed methods so far for the uniqueness examination—based on the modified mobility equation, the constraint matrix, or the free-body diagram—are not well suited for multibody systems described by relative coordinates. The novel method discussed in this paper breaks this limitation. The proposed approach is based on the divide-and-conquer algorithm (DCA)—a low-order recursive method for dynamic simulations of complex multibody systems. The devised method may be used for checking the joint-reaction uniqueness of holonomic systems with ideal constraints that fulfill some additional assumptions. The reaction-uniqueness analysis is performed when the main pass of the DCA is completed. An eight-step algorithm is proposed. In the case of the single-joint connections, it is sufficient to study the appropriate equations of motion. However, if the multijoint connection is present, then one of the numerical methods—known from the constraint-matrix-based or the free-body-diagram-based approach—has to be used, namely the rank-comparison, QR-decomposition, SVD, or nullspace methods; all of these approaches are discussed. To illustrate the devised method, a spatial parallelogram mechanism with a triple pendulum is analyzed.

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来源期刊
CiteScore
6.00
自引率
17.60%
发文量
46
审稿时长
12 months
期刊介绍: The journal Multibody System Dynamics treats theoretical and computational methods in rigid and flexible multibody systems, their application, and the experimental procedures used to validate the theoretical foundations. The research reported addresses computational and experimental aspects and their application to classical and emerging fields in science and technology. Both development and application aspects of multibody dynamics are relevant, in particular in the fields of control, optimization, real-time simulation, parallel computation, workspace and path planning, reliability, and durability. The journal also publishes articles covering application fields such as vehicle dynamics, aerospace technology, robotics and mechatronics, machine dynamics, crashworthiness, biomechanics, artificial intelligence, and system identification if they involve or contribute to the field of Multibody System Dynamics.
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